Alternative determinism principle for ...
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Alternative determinism principle for topological analysis of chaos
Auteur(s) :
Titre de la revue :
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Pagination :
035202(R)
Éditeur :
American Physical Society
Date de publication :
2006
ISSN :
1539-3755
Mot(s)-clé(s) en anglais :
chaos
entropy
knots
topology
simplicial spaces
entropy
knots
topology
simplicial spaces
Discipline(s) HAL :
Science non linéaire [physics]/Dynamique Chaotique [nlin.CD]
Résumé en anglais : [en]
The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core ...
Lire la suite >The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon which this approach is built, determinism and continuity, apply in any dimension. We propose an alternative framework in which these principles are enforced on triangulated surfaces rather than curves and show that in dimension three our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.Lire moins >
Lire la suite >The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon which this approach is built, determinism and continuity, apply in any dimension. We propose an alternative framework in which these principles are enforced on triangulated surfaces rather than curves and show that in dimension three our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Source :
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- http://arxiv.org/pdf/nlin.CD/0503006
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- https://hal.archives-ouvertes.fr/hal-00004359v3/document
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- https://hal.archives-ouvertes.fr/hal-00004359v3/document
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- knotless.pdf
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- 0503006
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